The combinatorial rigidity conjecture is false for cubic polynomials

Henriksen, Christian

doi:10.1090/S0002-9947-03-03259-8

The combinatorial rigidity conjecture is false for cubic polynomials
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by Christian Henriksen PDF

Trans. Amer. Math. Soc. 355 (2003), 3625-3639 Request permission

Abstract:

We show that there exist two cubic polynomials with connected Julia sets which are combinatorially equivalent but not topologically conjugate on their Julia sets. This disproves a conjecture by McMullen from 1995.

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